Transient Loss‐Induced Non‐Hermitian Degeneracies for Ultrafast Terahertz Metadevices

Abstract Non‐Hermitian degeneracies, also known as exceptional points (EPs), have attracted considerable attention due to their unique physical properties. In particular, metasurfaces related to EPs can open the way to unprecedented devices with functionalities such as unidirectional transmission and ultra‐sensitive sensing. Herein, an active non‐Hermitian metasurface with a loss‐induced parity‐time symmetry phase transition for ultrafast terahertz metadevices is demonstrated. Specifically, the eigenvalues of the non‐Hermitian transmission matrix undergo a phase transition under optical excitation and are degenerate at EPs in parameter space, which is accompanied by the collapse of chiral transmission. Ultrafast EP modulation on a picosecond time scale can be realized through variations in the transient loss at a non‐Hermitian metasurface pumped by pulsed excitation. Furthermore, by exploiting the physical characteristics of chiral transmission EPs, a switchable quarter‐wave plate based on the photoactive metasurface is designed and experimentally verified and realized the corresponding function of polarization manipulation. This work opens promising possibilities for designing functional terahertz metadevices and fuses EP physics with active metasurfaces.


Numerically extracted eigentransmission magnitudes and eigentransmission phases as a function of Ge conductivities from Riemannian surfaces
Fig. S1 Numerically extracted eigentransmission magnitudes (red solid lines) and phases (blue dashed lines) versus simulated Ge conductivities.The chain lines mark the frequency of 0.65 THz.The EP is found to be located at the frequency of 0.64THz and Ge conductivity of 1370 S/m.A crossing behavior in the magnitude and phase of eigenvalues reveals EP is located at the parameter space of ( , ,   ) = (0.64 , 1370 /).

Extracted eigentransmission magnitudes and phases versus time delay from experimental and simulated eigenvalue Riemann surfaces
To shed light on the temporal evolution dynamics of phase transition in non-Hermitian metasurface, we experimentally extract the eigentransmission magnitudes and phases with the time delay from 0 to 10.6 ps, shown in Fig. S2a.A crossing to anti-crossing transition containing the first EP at the critical point of ( , ,  , ) = (0.68 , 2.6 ) is clearly observable in the timeresolved eigenvalue curves.The second EP occurs at the frequency of 0.68 THz and the time delay of 8.9ps in opposite eigentransmission transition.The uncrossed eigentransmission magnitude in the regime of  <   at 0 ps and 10.6 ps comes from experimental errors and the frequency resolution.Similarly, numerically extracted eigentransmission magnitudes and phases with time delay from 0 to 14.9 ps are shown in Fig. S2b.The EPs appear at the critical points of ( , ,  , ) = (0.64 , 4.9 ) and ( , ,  , ) = (0.64 , 11.5 ).

Optical-pump terahertz-probe system and experimental scheme
Femtosecond plus laser in the optical path is generated by a Ti: sapphire regenerative amplifier system with 1 kHz repetition at a central wavelength of 800 nm.The terahertz generation and detection are completed by 1-mm-thick <110> ZnTe crystal.For measurement of polarization conversion when a terahertz wave passes through the Ge-hybrid non-Hermitian metasurface, one can obtain four linearly polarized components by rotating the sample and  2 .Besides,  1 and  4 are used to ensure that the terahertz wave is polarized in the y direction for emission and detection.By rotating  2 so that the polarization direction follows the x and y directions respectively, the transmission components of   and   can be obtained.And rotating the sample can represent the incident in two directions.The polarization direction of  3 is at a 45-degree angle to the y-axis, ensuring that both   and   can be detected.The terahertz spot with a diameter of 3 mm is focused on a 5 × 5 sample surface through a pair of parabolic mirrors.The pump light with a diameter of 5 mm is used to excite the conductivity of Ge film for modulation of the active non-Hermitian metasurface.

Fig. S2
Fig. S2 Extracted eigentransmission magnitudes and phases versus time delay from experimental and simulated eigenvalue Riemann surfaces.(a) The evolution process of the experimental measured eigentransmission magnitude (red solid lines) and phase (blue dashed lines) with time delays of 0, 2.6, 5.5, 8.9, and 10.6 ps.The chain lines mark the frequency of 0.7 THz.EPs are experimentally found at the time delays of 2.6 and 8.9 ps.(b) The evolution process of the numerical eigentransmission magnitude (red solid lines) and phase (blue dashed lines) with time delays of 0, 4.9, 8.2, 11.5, 14.9 ps.The chain lines mark the frequency of 0.65 THz.

Fig. S3
Fig. S3 Temporal evolution dynamics of the chiral transmission in the Ge-hybrid metasurface implemented by transient simulation.(a, b, c) The numerically simulated transmission magnitude of   (a),   (b), and   (c) as a function of pump-probe time delay.(d, e, f) The numerically simulated transmission phase of   (a),   (b), and   (c) as a function of pump-probe time delay.The metasurface system at EP shows asymmetric transmission, log (  ) ≠ log (  ) , and only the RCP component is transmitted for the input state with RCP, abs (  ) = 0, abs (  ) ≠ 0.

Fig
Fig. S4 A homemade optical pump terahertz-probe system for measurement of Ge-hybrid non-Hermitian metadevice.Four linearly polarized transmission signals were measured by rotating the sample and linear polarizer.LP: terahertz wire grid polarizer for linear polarization transmission.